Associative memory of weakly connected oscillators

It is a well-known fact that oscillatory networks can operate as Hopfield-like neural networks, the only difference being that their attractors are limit cycles: one for each memorized pattern. The neuron activities are synchronized on the limit cycles, and neurons oscillate with fixed phase differences (time delays). We prove that this property is a natural attribute of general weakly connected neural networks, and it is relatively independent of the equations that describe the network activity. In particular, we prove an analogue of the Cohen-Grossberg convergence theorem for oscillatory neural networks.